219k views
3 votes
Determine the solution to the differential equation -2 = -y with the initial condition y(0) = -3.

User Helvio
by
8.2k points

1 Answer

3 votes

Final answer:

To solve the differential equation -2 = -y with the initial condition y(0) = -3, we integrate both sides and apply the initial condition to find the constant of integration, yielding the solution y(t) = 2t - 3.

Step-by-step explanation:

To determine the solution to the differential equation -2 = -y with the initial condition y(0) = -3, we start by separating variables and integrating. Since the differential equation is already separated, we can integrate both sides with respect to t to solve for y. We immediately integrate to get y = 2t + C, where C is the constant of integration.

Now, we apply the initial condition to find C. We set y(0) equal to -3, which gives us -3 = 2(0) + C, so C = -3. Therefore, the solution to the differential equation is y(t) = 2t - 3.

User Abdelrahman Elkady
by
8.2k points